In October 2008, I submitted a prayer at the Prayer Request Site asking for a zero of the zeta function with real part different from 1/2. I gave to whomever fulfills these prayers (let's call it god) a deadline of a month. As the deadline is well over, I can now safely declare that
god told me that there all zeros of the zeta function have real part equal to 1/2; in other words, god told me that the Riemann Hypothesis is true.
An unsolved problem in Mathematics has been solved by the mere intervention of the owner of the Prayer Request Site, i.e. god. Isn't it amazing how prayer works?
Not being ungrateful, I submitted a thank you note at the Prayer Request Site:
PRAISE THE LORD!
Thank you for showing me that the Riemann Hypothesis is true: all zeros of the zeta function have real part equal to 1/2. Can you please help me write a paper now? Or is it sufficient to simply declare that you told me so?
30 December 2008
29 December 2008
Saint Joseph Stalin
A couple of years ago, a certain Aleksandr Filippov wrote a history textbook, titled “Russian History, 1945-2007”, for Russian schoolchildren. In it, he returns to an almost Soviet view of Stalin's legacy, claiming that there were "rational reasons behind the use of violence [by Stalin] in order to ensure maximum efficiency". Stalin is being hailed as an efficient manager who [merely] had to resort to extreme measures to modernize the lumbering of Soviet agrarian economy.
In a review of the textbook by Irina Karatsuba, historian and associate professor in the Department of Regional Studies at Moscow State University, we read that "this was without doubt a paid-for textbook, written on someone’s orders, phony all the way through", that "Putin is the second most effective leader the country has ever had, after Stalin".
There is, indeed, a movement in Russia aiming towards the rehabilitation of Stalin. Putin himself is, certainly, behind it. Recall that Putin's dream is to be buried next to Stalin. In the revisionist scheme, the Orthodox Church cannot remain indifferent. Indeed, icons of Stalin have already appeared:
The icon on the left shows Stalin standing before the Blessed Matrona of Moscow, a 20th-century saint. According to legend, Stalin would frequently talk to the woman who gave him advice on how to defeat Nazi Germany in World War II.
The icon on the right depicts Stalin himself as a Saint.
Absurdities? Stupidities? Irrational acts? Indeed, all of the above and more. Revising history happens all the time in all countries. Even if we now, most of us, see the aforementioned revision as totally irrational, it may, in the end, become the norm: if a lie keeps being propagated by an official source for long time then it persists; people forget and the next generation is brought up starting from different initial conditions. And we all know that getting rid of (bad) initial conditions is tough.
Endnotes
1.Irina Karatsuba's review: This past summer I read this textbook in detail and took part in a round table discussion organized by the journal “Bolshoi Gorod” in which the textbook was discussed. After studying Filippov’s textbook and discussing it with the authors, I came to the inescapable conclusion that this was without doubt a paid-for textbook, written on someone’s orders, phony all the way through. It is based on one very dangerous idea, which can be summed up succinctly as, “The State is everything, the individual nothing.” Regarding the current regime, the textbook is absolutely servile, stating simply that Putin is the second most effective leader the country has ever had, after Stalin. And this is the crowning glory - there is nowhere higher to go. For this reason, of course, its introduction into schools in any capacity (and I think it will be introduced, as the leading textbook) can bring only harm.
2. Another example of history revisionism: Almost every Greek will now tell you that the revolution against the Ottomans has started from within the Church and that the Bishop Germanos of Patras (Georgios Gotzias 1771-1826) proclaimed the national uprising on 25 March 1821 (national day of Greece). This is a mere myth. The truth is that the Greek Church did not want any uprising at all because the priests had a special status in the Ottoman Empire as tax collectors and hence benefiting themselves from the money deals with the Turks. In fact, when Patriarch Gregory V (Georgios Angelopoulos 1746-1821) failed to suppress the revolution, the Turks hung him. The Greek State revised the history, and now this Patriarch is now a Saint of the Orthodox Church. (To be fair, it is true that the hanging of the Patriarch was, indeed, perceived as an atrocious act amongst Greeks and did help in creating a national sentiment, so, indirectly, it did help the uprising. But it seems that the Patriarch himself had no intention of supporting a revolution against the Turks.)
In a review of the textbook by Irina Karatsuba, historian and associate professor in the Department of Regional Studies at Moscow State University, we read that "this was without doubt a paid-for textbook, written on someone’s orders, phony all the way through", that "Putin is the second most effective leader the country has ever had, after Stalin".
There is, indeed, a movement in Russia aiming towards the rehabilitation of Stalin. Putin himself is, certainly, behind it. Recall that Putin's dream is to be buried next to Stalin. In the revisionist scheme, the Orthodox Church cannot remain indifferent. Indeed, icons of Stalin have already appeared:
The icon on the left shows Stalin standing before the Blessed Matrona of Moscow, a 20th-century saint. According to legend, Stalin would frequently talk to the woman who gave him advice on how to defeat Nazi Germany in World War II.
The icon on the right depicts Stalin himself as a Saint.
Absurdities? Stupidities? Irrational acts? Indeed, all of the above and more. Revising history happens all the time in all countries. Even if we now, most of us, see the aforementioned revision as totally irrational, it may, in the end, become the norm: if a lie keeps being propagated by an official source for long time then it persists; people forget and the next generation is brought up starting from different initial conditions. And we all know that getting rid of (bad) initial conditions is tough.
Endnotes
1.Irina Karatsuba's review: This past summer I read this textbook in detail and took part in a round table discussion organized by the journal “Bolshoi Gorod” in which the textbook was discussed. After studying Filippov’s textbook and discussing it with the authors, I came to the inescapable conclusion that this was without doubt a paid-for textbook, written on someone’s orders, phony all the way through. It is based on one very dangerous idea, which can be summed up succinctly as, “The State is everything, the individual nothing.” Regarding the current regime, the textbook is absolutely servile, stating simply that Putin is the second most effective leader the country has ever had, after Stalin. And this is the crowning glory - there is nowhere higher to go. For this reason, of course, its introduction into schools in any capacity (and I think it will be introduced, as the leading textbook) can bring only harm.
The textbook automatically brings to mind how we all once studied. Soviet textbooks contained not a word of truth, of course, and no one took them seriously, nor did they expect to learn anything from the subject of history, but searched for the truth instead on their own. I recall how a textbook I was once studying (I graduated from high school in 1977) said that “the careerist Ezhov and the political adventurist Beria, using some of Stalin’s personal marks, fabricated accusations that resulted in the deaths of tens of thousands of Communists.” Reading this, at age 16, I thought to myself: But how could these two people, with the help of a third, kill tens of thousands of people… What kind of regime was this? I think this is about the line of thought that will be followed by those who study from Filippov’s textbook.
But for me, as a professional, this is of course sad, because it is not just a step backward, but ten steps backward in comparison with the textbooks that were written at the end of the 1990’s and the beginning of this decade. And I am very bitter about how the textbooks of Dolutskiy and other authors are being replaced with nonsense like this.
This event is not, of course, unique. It is part of a general process of searching for a new Russian identity. A reconsideration of the Soviet period is taking place, expelling the odious waste of “the terrible 1990s” (although the current occupants of the our political
I would also recall the words of Petr Chaadaev, who wrote in 1837 that “The era of blind belief has passed. I think that now the truth is our greatest obligation to the Motherland.” Alas, this was such a premature hope, because even today this “now” has not yet arrived. But what will become of our Motherland, and of the truth, if this “now” never arrives?
2. Another example of history revisionism: Almost every Greek will now tell you that the revolution against the Ottomans has started from within the Church and that the Bishop Germanos of Patras (Georgios Gotzias 1771-1826) proclaimed the national uprising on 25 March 1821 (national day of Greece). This is a mere myth. The truth is that the Greek Church did not want any uprising at all because the priests had a special status in the Ottoman Empire as tax collectors and hence benefiting themselves from the money deals with the Turks. In fact, when Patriarch Gregory V (Georgios Angelopoulos 1746-1821) failed to suppress the revolution, the Turks hung him. The Greek State revised the history, and now this Patriarch is now a Saint of the Orthodox Church. (To be fair, it is true that the hanging of the Patriarch was, indeed, perceived as an atrocious act amongst Greeks and did help in creating a national sentiment, so, indirectly, it did help the uprising. But it seems that the Patriarch himself had no intention of supporting a revolution against the Turks.)
24 December 2008
Gallica
Gallica is the Interner digital library of the National Library of France. It was established more than 10 years ago. To-date, it hosts about one hundred thousand books, most in scanned form. Everything is available for free. It is a treasure for those who do not have direct access to the original sources, such as the works of Henri Poincare (see e.g. `La Valeur de la Science'). There is a lot of information out there, but verylittle time. A few thoughts come in mind: (1) How can we use the information efficiently? (2) It is, after all, true that our hours are minutes when we wait to learn and centuries when we know what is to be learnt, as António Machado says.
Incidentally, Newton's birthday (the image above is from one of his major works) is tomorrow, 25 December.
17 December 2008
New high tech game
A new family game has just made its appearance on the Internet. It's a perfect Christmas activity for the whole family:
As of 17 December 2008, 13:30, more than 7 million shoes have successfully hit Dubya.
As of 17 December 2008, 13:30, more than 7 million shoes have successfully hit Dubya.
15 December 2008
The h factor
Academic and research administrators have an interest in reducing one's work into a single number. Ideally, they claim, they could use a single number to decide whether researcher A is better than researcher B. The actual reasons behind such claims are that the majority of administrators (academic department chairmen, directors funding agencies, heads of laboratories, etc) cannot understand each researcher's work, and also want to minimize their time in giving a judgment: they can, with the click of a button, order researchers in a line a button and finish their work in five minutes.
In fact, there is a "science" being developed, called "bibliometrics" (see here, here, here and here) aiming at producing such indices. The most (in)famous of these indices is the h factor (not the x factor--this is a TV programme--see below). The h factor is defined as follows: If a researcher has n papers cited n times each then his or her h factor is at least n. In fact the h factor is the largest such n.
For example, if a researcher has written one paper which is cited 1000 times and 9 other papers which are cited once each then his h factor is 1. If researcher B has written 3 papers, each cited twice, then her h factor is 2. Hence B is better than A (an administrator would conclude).
A recent report by Robert Adler (Probabilist of the Technion–Israel Institute of Technology), John Ewing (Executive Director, American Mathematical Society, and Peter Taylor (Probabilist, University of Melbourne) show that "citation data provide only a limited and incomplete view of research quality, and the statistics derived from citation data are sometimes poorly understood and misused; [r]esearch is too important to measure its value with only a single coarse tool". It's an interesting read.
However, I admit that the report may not be as much fun as an x factor episode:
Just to make things clear, the guy in this video is not looking for an h factor, but an x factor. (Some colleagues tell me it's more or less the same thing though.)
In fact, there is a "science" being developed, called "bibliometrics" (see here, here, here and here) aiming at producing such indices. The most (in)famous of these indices is the h factor (not the x factor--this is a TV programme--see below). The h factor is defined as follows: If a researcher has n papers cited n times each then his or her h factor is at least n. In fact the h factor is the largest such n.
For example, if a researcher has written one paper which is cited 1000 times and 9 other papers which are cited once each then his h factor is 1. If researcher B has written 3 papers, each cited twice, then her h factor is 2. Hence B is better than A (an administrator would conclude).
A recent report by Robert Adler (Probabilist of the Technion–Israel Institute of Technology), John Ewing (Executive Director, American Mathematical Society, and Peter Taylor (Probabilist, University of Melbourne) show that "citation data provide only a limited and incomplete view of research quality, and the statistics derived from citation data are sometimes poorly understood and misused; [r]esearch is too important to measure its value with only a single coarse tool". It's an interesting read.
However, I admit that the report may not be as much fun as an x factor episode:
Just to make things clear, the guy in this video is not looking for an h factor, but an x factor. (Some colleagues tell me it's more or less the same thing though.)
4 December 2008
Happy Newtonmas cards
I designed some cards for the season. Please feel free to copy, print on hard paper, and send them around. There is a front side and a back side which should be glued together. Depending on taste, you may pick any of the front side versions.
28 November 2008
26 November 2008
God Trumps: a family card game
Christmas is in the air. You walk down high street and you are bombarded with all kinds of festive songs, ranging from Rudolph the Red-Nose Reindeer to God Rest Ye Merry Gentlemen and the like. Like it or not, you are bound to hear the same music hundreds of times. It is, after all, the festive season, the season to spend your money, and the music, according to marketing researches, helps you do that. Christmas lasts now about two months each year (1/6 of the year). Christmas needs Gemütlichkeit, everyone around the fireplace (regardless of the temperature outside), and Glühwein, and food and, of course, family games! One of the best games around this season is God Trumps, invented by the New Humanist. It is designed to help the whole family choose the right religion. It's a card game. To play it, print the cards at size 63 mm × 88 mm (or B8 size) and glue on old playing cards or cardboard. (Some family activity too!) The rules are extremely simple and need not be added here for fear of insulting your intelligence.
As an added twist to the game, you may:
(i) Add your own religion. Who knows? You may be a success! And why not? A religion is something that can be invented and changed. The concept of a time-varying religion should seriously be studied in institutions of higher learning hosting schools of theology or divinity.
(ii) Copy the cards many times. Have a stock of dozens of each one and, depending on the way the game goes, see which cards are become dominant. Perhaps this will be an indication of the new cool religionof the year.
(iii) Invite your neighbours. Get involved in outreach activities. Play with your friends, make sure the game is spread all over the town, the country, the world!
(iv) Write to Tony Blair and ask him to adopt it as part of his course at Yale.
As an added twist to the game, you may:
(i) Add your own religion. Who knows? You may be a success! And why not? A religion is something that can be invented and changed. The concept of a time-varying religion should seriously be studied in institutions of higher learning hosting schools of theology or divinity.
(ii) Copy the cards many times. Have a stock of dozens of each one and, depending on the way the game goes, see which cards are become dominant. Perhaps this will be an indication of the new cool religionof the year.
(iii) Invite your neighbours. Get involved in outreach activities. Play with your friends, make sure the game is spread all over the town, the country, the world!
(iv) Write to Tony Blair and ask him to adopt it as part of his course at Yale.
23 November 2008
Deep faith
This is a video about praying in unison. No comments will be added. Just watch and see what Goya meant when he said "the sleep of reason creates monsters". This is what faith is about, and what you see here is not an isolated phenomenon. Alas, there are far too many men and women of faith who practice these things. I wonder what Blair thinks about them when he teaches faith at Yale University...
21 November 2008
No to Guantánamo, Yes to Guantanamera
“As President, I will
close Guantánamo,
reject the Military Commissions Act, and adhere to the Geneva Conventions”
– Barack Obama, 8/1/07
Therefore, now that he is president, we ask him: Close Guantánamo and end military commissions. In fact, let Guantánamo be a place where guantanamera comes from; it is songs we need, no war, no torture, no hatred:
18 November 2008
Silly maths quiz at BBC site
Marcus du Sautoy, the man who will succeed Richard Dawkins as professor for the understanding of science at the University of Oxford, has a mission to break down people's fear of maths. So he set up a quiz. Unfortunately, the quiz is rather naive and does not reflect what mathematics is about. Here are some dubious questions:
* A temple was built in 50 BC and burnt down 75 years later. In what year whas it burnt down?
(1) 24 AD. (2) 25 AD. (3) 26 AD.
The logical thinking gives -50+75=+25, i.e. 25 AD (provided that both events took place on the same day of the year, say on day 1.)
But the answer given by the BBC is: 26 AD. There was no year 0.
This is a fact, indeed: that there was no year 0. Some 1500 years ago, a monk called Dionisius Exiguus was charged with the creation of a calendar; this monk did not know that the integer succeeding -1 is 0 and not +1; i.e. he thought that -1+1=1.
But the ignorance of a monk should not be brought into a mathematical quiz which, supposedly, tests one's understanding of logic (and not of history!)
* Imagine picking up a cube with your thumb placed at one corner of the cube and your finger at the furthest corner on the other side of the cube. Now cut the cube exactly down the middle between your finger and thumb. You have two pieces with a new face. What is the shape of the new face?
(1) Hexagonal. (2) Square. (3) Triangular.
Before looking at the answer let us look at the way the problem is phrased. First, what exactly is meant by a corner? Is it a vertex? Is it an edge? I think he means a vertex, i.e. the point at which 3 faces meet. But it could be an edge: the segment at which 2 faces meet forms a corner, in my humble opinion, too. The answer will of course, be different depending on the interpretation of the word corner. OK, let us assume he means a vertex. Now what does he mean by "cut the cube exactly down the middle"? This could also mean a number of things. Here we must guess that he means to take the plane that is perpendicular to the segment joining two vertices at farthest distant appart and which passes through the middlepoint of this segment. This plane intersects the (boundary of the) cube at a polygon. And this polygon is, indeed, a hexagon.
But a mathematical question should be phrased in an unambiguous way!
* What is the next number in the sequence 1001, 122, 101, 32, 25, 23, 21, ...
(1) 20. (2) 18. (3) 15.
Again, this is a dangerous question for the mathematically uninitiated for he or she may think that there is a unique choice. For instance, if I give you the sequence 1,4,8,16,32,64,128 you might think that the next number is 256 (powers of 2). But a perfectly acceptable answer is 144. (Indeed, if we let p(m) be the product of the exponents in the prime factorisation of m, and define q(n) to be to be the smallest integer such that p(q(n))=n then q(1)=1, q(2)=4,...,q(7)=128, but q(8)=144.)
Now then, the answer to this question, according to BBC, but also according to the encyclopedia of integer sequences, is 18: if we write the number 17 in base 2 we get 1001, in base 3 it is 122, and so on.
But hang on a minute! This is by far NOT a fair question and a misleading one for the two reasons I outlined: first, it gives the wrong impession on what Mathematics is about. Second, the answer is hard and, clearly, not unique.
* A temple was built in 50 BC and burnt down 75 years later. In what year whas it burnt down?
(1) 24 AD. (2) 25 AD. (3) 26 AD.
The logical thinking gives -50+75=+25, i.e. 25 AD (provided that both events took place on the same day of the year, say on day 1.)
But the answer given by the BBC is: 26 AD. There was no year 0.
This is a fact, indeed: that there was no year 0. Some 1500 years ago, a monk called Dionisius Exiguus was charged with the creation of a calendar; this monk did not know that the integer succeeding -1 is 0 and not +1; i.e. he thought that -1+1=1.
But the ignorance of a monk should not be brought into a mathematical quiz which, supposedly, tests one's understanding of logic (and not of history!)
* Imagine picking up a cube with your thumb placed at one corner of the cube and your finger at the furthest corner on the other side of the cube. Now cut the cube exactly down the middle between your finger and thumb. You have two pieces with a new face. What is the shape of the new face?
(1) Hexagonal. (2) Square. (3) Triangular.
Before looking at the answer let us look at the way the problem is phrased. First, what exactly is meant by a corner? Is it a vertex? Is it an edge? I think he means a vertex, i.e. the point at which 3 faces meet. But it could be an edge: the segment at which 2 faces meet forms a corner, in my humble opinion, too. The answer will of course, be different depending on the interpretation of the word corner. OK, let us assume he means a vertex. Now what does he mean by "cut the cube exactly down the middle"? This could also mean a number of things. Here we must guess that he means to take the plane that is perpendicular to the segment joining two vertices at farthest distant appart and which passes through the middlepoint of this segment. This plane intersects the (boundary of the) cube at a polygon. And this polygon is, indeed, a hexagon.
But a mathematical question should be phrased in an unambiguous way!
* What is the next number in the sequence 1001, 122, 101, 32, 25, 23, 21, ...
(1) 20. (2) 18. (3) 15.
Again, this is a dangerous question for the mathematically uninitiated for he or she may think that there is a unique choice. For instance, if I give you the sequence 1,4,8,16,32,64,128 you might think that the next number is 256 (powers of 2). But a perfectly acceptable answer is 144. (Indeed, if we let p(m) be the product of the exponents in the prime factorisation of m, and define q(n) to be to be the smallest integer such that p(q(n))=n then q(1)=1, q(2)=4,...,q(7)=128, but q(8)=144.)
Now then, the answer to this question, according to BBC, but also according to the encyclopedia of integer sequences, is 18: if we write the number 17 in base 2 we get 1001, in base 3 it is 122, and so on.
But hang on a minute! This is by far NOT a fair question and a misleading one for the two reasons I outlined: first, it gives the wrong impession on what Mathematics is about. Second, the answer is hard and, clearly, not unique.
13 November 2008
The BLAFAFO = Blair Faith Foundation
Does this man look possessed?
You betcha! He is possessed by such a stupidity that, earlier this year, he declared that faith must be given a central role in tackling the world's problems. Faith? Have I heard well? Indeed, faith! This is a person who has not lived in the middle ages. Rather, he is alive and well now, in the 21st century, enjoying his benefits as the ex-prime minister of the UK. No sooner had he finished his career, than he ran to the Pope and asked him to transform him to a Christian Catholic (I suppose he had been worshiping a different version of Christianity before, hence he did need a transformation). Immediately after, he gave a speech at the Westminster Cathedral. He said he is a man of faith and that his faith has influenced his politics. In other words, he came out of the closet: Whereas his buddy Dubya has been saying out loud all along that God tells him what to do, Tony has been a bit more shy about his tendencies. We now know he has had exactly the same orientation as Dubya, but it took him long time to declare his pride with pride, which is what he does now, clearly and openly:
"Religious faith is a good thing in itself that so far from being a reactionary force - it is a major part to play in shaping values which guide the modern world and can and should be a force for progress."
So, for Anthony Blair, faith is a force of progress! In other words, with one sentence he wipes out all scientific progress, all rational thought, he decides to embrace the darkness of unreason, to get rid of enlightenment... And guess what he does. He knows he can't quite find sympathy for his stupidity in the UK so he goes to the land of the blessed ones, America, and establishes the Tony Blair Fath Foundation! There he finds sponsors who supply him with dollars to use as he wishes. He also practices mind-fucking at Yale University. (Is it a coincidence that Yale is also the school where Dubya "studied"?) He is teaching a 3-year course at the Yale Divinity School and Management School. (What on earth is the connection between the supernatural and management, only God knows, and, I suppose, this is what Blair is now talking about, having obtained direct links to God--his previous links were indirect, i.e. through his Dubya.) Rumour has it that Yale offered to his offspring, Euan Blair, more money than Harvard (92,000 bucks), in order that both father and son go to Yale rather than Harvard. (I suppose this must have strengthened Tony's faith, for miracles like this happen only to those who believe.)
Now guess who introduced Blair at his Faith Foundation ceremony. You have only one guess. "Dubya!" you reply. Wrong! You lose! Why, it is Bill, Bill Clinton himself! (Another man of faith, I take it.):
And if you were thinking of going to the movies tonight, spare your money and click below instead (as well as related links on you tube): The comedy of Tony Blair in all its glory (and idiocy)!
You betcha! He is possessed by such a stupidity that, earlier this year, he declared that faith must be given a central role in tackling the world's problems. Faith? Have I heard well? Indeed, faith! This is a person who has not lived in the middle ages. Rather, he is alive and well now, in the 21st century, enjoying his benefits as the ex-prime minister of the UK. No sooner had he finished his career, than he ran to the Pope and asked him to transform him to a Christian Catholic (I suppose he had been worshiping a different version of Christianity before, hence he did need a transformation). Immediately after, he gave a speech at the Westminster Cathedral. He said he is a man of faith and that his faith has influenced his politics. In other words, he came out of the closet: Whereas his buddy Dubya has been saying out loud all along that God tells him what to do, Tony has been a bit more shy about his tendencies. We now know he has had exactly the same orientation as Dubya, but it took him long time to declare his pride with pride, which is what he does now, clearly and openly:
"Religious faith is a good thing in itself that so far from being a reactionary force - it is a major part to play in shaping values which guide the modern world and can and should be a force for progress."
So, for Anthony Blair, faith is a force of progress! In other words, with one sentence he wipes out all scientific progress, all rational thought, he decides to embrace the darkness of unreason, to get rid of enlightenment... And guess what he does. He knows he can't quite find sympathy for his stupidity in the UK so he goes to the land of the blessed ones, America, and establishes the Tony Blair Fath Foundation! There he finds sponsors who supply him with dollars to use as he wishes. He also practices mind-fucking at Yale University. (Is it a coincidence that Yale is also the school where Dubya "studied"?) He is teaching a 3-year course at the Yale Divinity School and Management School. (What on earth is the connection between the supernatural and management, only God knows, and, I suppose, this is what Blair is now talking about, having obtained direct links to God--his previous links were indirect, i.e. through his Dubya.) Rumour has it that Yale offered to his offspring, Euan Blair, more money than Harvard (92,000 bucks), in order that both father and son go to Yale rather than Harvard. (I suppose this must have strengthened Tony's faith, for miracles like this happen only to those who believe.)
Now guess who introduced Blair at his Faith Foundation ceremony. You have only one guess. "Dubya!" you reply. Wrong! You lose! Why, it is Bill, Bill Clinton himself! (Another man of faith, I take it.):
And if you were thinking of going to the movies tonight, spare your money and click below instead (as well as related links on you tube): The comedy of Tony Blair in all its glory (and idiocy)!
No freedom of speech in Turkey
A Turkish court has banned internet users from viewing the official Richard Dawkins website after a Muslim creationist, Adnan Oktar (pen name: Harun Yahya)
claimed its contents were defamatory and blasphemous. Story here.
Adnan Oktar is a Muslim creationist. Creationists (also known as intelligent designers) are light-headed people who deny Darwin's view of evolution, as well as many other scientific facts, such as the age of the Universe, the fact that the Earth is round (some think the Earth is flat). Typically, creationists are Christian fundamentalists. But here we see that creationists exist amongst Muslims as well. That this event happened in Turkey is not surprising because Turkey has a long track record in banning websites, and is particularly fond of blocking YouTube for allegedly offending national sensibilities. The bans have hurt its image at a time when its restrictions on free speech are under scrutiny owing to its EU membership bid.
It is very sad that the Turkish government, under the pressure of a fundamentalist, decided to ban Dawkins' site. Free speech should mean free speech, regardless of whether you agree with it or not. Banning a source of information is not what the 21st century is supposed to be about.
Note, added on 25/11/o8:
This guy is now offering some 50,000 euros for an essay on why evolution is false:
You have about a year to right some idiocy and send it to the so called (euphemistically) Research Science Foundation, Çakırağa mah, Katip Müslihittin sok, Sağlam İşhanı No.3 D.12-13 Aksaray/İstanbul.
claimed its contents were defamatory and blasphemous. Story here.
Adnan Oktar is a Muslim creationist. Creationists (also known as intelligent designers) are light-headed people who deny Darwin's view of evolution, as well as many other scientific facts, such as the age of the Universe, the fact that the Earth is round (some think the Earth is flat). Typically, creationists are Christian fundamentalists. But here we see that creationists exist amongst Muslims as well. That this event happened in Turkey is not surprising because Turkey has a long track record in banning websites, and is particularly fond of blocking YouTube for allegedly offending national sensibilities. The bans have hurt its image at a time when its restrictions on free speech are under scrutiny owing to its EU membership bid.
It is very sad that the Turkish government, under the pressure of a fundamentalist, decided to ban Dawkins' site. Free speech should mean free speech, regardless of whether you agree with it or not. Banning a source of information is not what the 21st century is supposed to be about.
Note, added on 25/11/o8:
This guy is now offering some 50,000 euros for an essay on why evolution is false:
You have about a year to right some idiocy and send it to the so called (euphemistically) Research Science Foundation, Çakırağa mah, Katip Müslihittin sok, Sağlam İşhanı No.3 D.12-13 Aksaray/İstanbul.
10 November 2008
Orthodoxy makes front page news (again)
Fighting erupted between Greek Orthodox and Armenian monks at the Church of the Holy Sepulchre, the traditional site of Christ's crucifixion in Jerusalem's Old City. Israeli police have had to restore order after a mass brawl broke out between monks. Stories here and here.
Several similar incidences have occurred in the past:
On Palm Sunday, in April 2008, a brawl broke out due to a Greek monk being ejected from the building by a rival faction. Police were called to the scene but were also attacked by the enraged brawlers. Story here.
In 2004 during Orthodox celebrations of the Exaltation of the Holy Cross, a door to the Franciscan chapel was left open. This was taken as a sign of disrespect by the Orthodox and a fistfight broke out and some people were arrested. Story here.
In 2002 Ethiopian and Copt monks threw stones at each other over rights to the church roof.
Honestly, I don't understand what they are fighting for. One sect wants a monk placed inside a room, the other does not. Or a door is left open... What's the big deal? Well, go figure... In matters of religion, trying to understand is not the thing to do.
Several similar incidences have occurred in the past:
On Palm Sunday, in April 2008, a brawl broke out due to a Greek monk being ejected from the building by a rival faction. Police were called to the scene but were also attacked by the enraged brawlers. Story here.
In 2004 during Orthodox celebrations of the Exaltation of the Holy Cross, a door to the Franciscan chapel was left open. This was taken as a sign of disrespect by the Orthodox and a fistfight broke out and some people were arrested. Story here.
In 2002 Ethiopian and Copt monks threw stones at each other over rights to the church roof.
Honestly, I don't understand what they are fighting for. One sect wants a monk placed inside a room, the other does not. Or a door is left open... What's the big deal? Well, go figure... In matters of religion, trying to understand is not the thing to do.
7 November 2008
Leave science alone
Here is a 21st century phenomenon: religious morons (ab)using science to prove that god exists, and, more specifically, the particular version of the god they believe in. I shall come back to this important new technique of religious bigots, but, for now, here is an example. The book of some R. D. Duncan discusses "[t]he periodic table of elements presented as never before! The tiniest elements that make up the world are more than just scientific odds and ends. Each and every one is an opportunity to celebrate the power, wisdom, order, and ingenuity of our Creator!". I searched to find out about the qualifications of this Duncan, but I had no luck. Surely, knowledge of Chemistry if not important for such books. But a dose of idiocy and blind faith certainly is. What a bunch of balloney!
But, hang on a minute. If you think this is to hard to digest, then how about the easier version, God’s Design for Chemistry, designed for grades 3–7, or the even easier one, God’s Design for Life, for grades 1-6 (both published by Answers in Genesis–US)?
If this is not mind-fucking, then what is?
Fine, one could argue, let those religious bigots, like Duncan, publish their books and circulate it amongst their circles. These authors have no scientific credentials, so they won't be taken seriously. But a more major problem is posed by those who do have scientific credentials and do try to promote (their version of) god and (their version of) religion by (ab)using their scientific titles in order to deceive laymen? An example of people in this category is Dr John Lennox of Oxford, who, by claiming his authority as a mathematician (an algebraist in fact working on finite groups), produces naive and childish arguments and books to prove that science implies that (his version of) god exists and that (his version of) religion is true. More on this soon...
But, hang on a minute. If you think this is to hard to digest, then how about the easier version, God’s Design for Chemistry, designed for grades 3–7, or the even easier one, God’s Design for Life, for grades 1-6 (both published by Answers in Genesis–US)?If this is not mind-fucking, then what is?
Fine, one could argue, let those religious bigots, like Duncan, publish their books and circulate it amongst their circles. These authors have no scientific credentials, so they won't be taken seriously. But a more major problem is posed by those who do have scientific credentials and do try to promote (their version of) god and (their version of) religion by (ab)using their scientific titles in order to deceive laymen? An example of people in this category is Dr John Lennox of Oxford, who, by claiming his authority as a mathematician (an algebraist in fact working on finite groups), produces naive and childish arguments and books to prove that science implies that (his version of) god exists and that (his version of) religion is true. More on this soon...
6 November 2008
"Living in Texas feels like being in a big prison"
This is what I used to say when I lived in Austin, Texas. And here is a proof:
Do you see the blue spec in the middle called Austin? It's sunk in a sea of reactionary red. (Just as a few other places.) You venture outside it and you're in the land of intolerance, the land of people whose law is based on guns and the Bible, the land of those who voted for McCain (and Dubya and his father in the past). Try to speak and you fear for your life. Despite appearances, this land is one of the most fundamentalist places in the world. There is no freedom of speech, no freedom of expression. Waco and Huntsville (were people get executed all the time) are typical of Texas. If you are different you can't stay. You may be killed. So you end up spending all the time in Austin, feeling, exactly, like being in a huge prison. This is why I used to use this phrase.
Do you see the blue spec in the middle called Austin? It's sunk in a sea of reactionary red. (Just as a few other places.) You venture outside it and you're in the land of intolerance, the land of people whose law is based on guns and the Bible, the land of those who voted for McCain (and Dubya and his father in the past). Try to speak and you fear for your life. Despite appearances, this land is one of the most fundamentalist places in the world. There is no freedom of speech, no freedom of expression. Waco and Huntsville (were people get executed all the time) are typical of Texas. If you are different you can't stay. You may be killed. So you end up spending all the time in Austin, feeling, exactly, like being in a huge prison. This is why I used to use this phrase.
5 November 2008
Good riddance Dubya
The all-time loser in presidential history will be remembered as the worst president of the US. This is what Simon Schama wrote yesterday in the Guardian, adding that not even McCain wanted to be seen as having anything to do with this idiot when he declared "I am not George Bush" in his final debate. Clearly, McCain didn't manage to dissociate himself too much from Dubya, and this resulted in his declaration, along the hockey mom, of defeat today. We are all worried, says the Guardian today, what kind of job will Dubya be capable of doing in 77 days from today. Because he's a man of action, he won't want to retire. The Guardian proposes the following jobs for W:
The new Doctor Who,
Leader, North Korea
Presenter, Friday Night with Dubya
Tour guide, presidential library
Manager, Watford FC
Star, W: the Musical
Interior minister, Iran
Paris Hilton's new best friend
Presenter, Top Gear
Sarah Palin's running mate, 2012
Biographer, George Bush Sr.
But no matter what job he does, he will be remembered, in our hearts, as the prime example of the a good-old malakas.Leader, North Korea
Presenter, Friday Night with Dubya
Tour guide, presidential library
Manager, Watford FC
Star, W: the Musical
Interior minister, Iran
Paris Hilton's new best friend
Presenter, Top Gear
Sarah Palin's running mate, 2012
Biographer, George Bush Sr.
24 October 2008
Prayer request
I just submitted a prayer at the Prayer Request Site. It goes like this:
Please show me a zero of the Riemann zeta function that has real part not equal to 1/2. I know that my prayer will be answered soon, as you say, in less than a month. If within a month I receive no reply to my prayer then I will know that the Riemann hypothesis is true. And therefore I can go out and claim that God told me it is so. If people ask me for a proof I will refer them to your site.
If I get a response then I will know that the Riemann hypothesis is false. If I don't then I will know it is true. Either way, I'm a winner and, I suppose, I can publish a paper titled "the Riemann hypothesis via Prayer Request Site". I will let you know what happens in a month or so.
For your information, other prayer request sites appear here. An amusing one is by the Celebrity Spotlight Ministries. In it, it is claimed that "the prayer of a righteous man is powerful and effective", followed by a picture of a mass-murderer. The most important message of the Celebrity Ministries prayer site is "PUSH". In other words, Pray Until Something Happens. (If this appears as an obvious tautology, it is because it really is.)
----
Update: As of to-date (11/11/08), my prayer has not been answered. So I prayed again:
I am really hoping it will be answered. The prayer request site
has direct links with the supernatural. You click it and then you communicate with the gods. Please go there and pray. It is fun! You don't need to work any more. Just pray for money. You don't need to worry any more. Just pray for happiness. In my case, I don't need to think about proofs any more. I will pray for theorems to be proved!
Please show me a zero of the Riemann zeta function that has real part not equal to 1/2. I know that my prayer will be answered soon, as you say, in less than a month. If within a month I receive no reply to my prayer then I will know that the Riemann hypothesis is true. And therefore I can go out and claim that God told me it is so. If people ask me for a proof I will refer them to your site.
If I get a response then I will know that the Riemann hypothesis is false. If I don't then I will know it is true. Either way, I'm a winner and, I suppose, I can publish a paper titled "the Riemann hypothesis via Prayer Request Site". I will let you know what happens in a month or so.
For your information, other prayer request sites appear here. An amusing one is by the Celebrity Spotlight Ministries. In it, it is claimed that "the prayer of a righteous man is powerful and effective", followed by a picture of a mass-murderer. The most important message of the Celebrity Ministries prayer site is "PUSH". In other words, Pray Until Something Happens. (If this appears as an obvious tautology, it is because it really is.)
----
Update: As of to-date (11/11/08), my prayer has not been answered. So I prayed again:
I am really hoping it will be answered. The prayer request site
has direct links with the supernatural. You click it and then you communicate with the gods. Please go there and pray. It is fun! You don't need to work any more. Just pray for money. You don't need to worry any more. Just pray for happiness. In my case, I don't need to think about proofs any more. I will pray for theorems to be proved!
22 October 2008
Conventions and rationality
One of the basic problems is the inability of many to recognise the difference between something that is fundamental and something that is a convention.
An example of a fundamental truth is the inverse square law of gravity. It is an empirical fact, based on observation, experiment, measurements; by accepting it, we build a theory upon which we can predict other facts, understand why it takes about 365 days for the earth to go around the sun, and build satellites, among other things. This is why the law of gravity is fundamental.
An example of a convention is that a week has seven days. It surprises many people that the concept of a week is not a concept, but a rather arbitray convention. It is difficult for many to digest this because the concept has been around for, well, some four thousand years. Of course, there are many a posteriori justifications. Why, say some, the week consists of seven days because the Bible says so. This is not a justification, even if the Bible was written by a God, as many contend.
The inability to distinguish between a fundamental truth and a convention is a major problem. It suddens me to have to point this out to my students (and others), in the post-enlightenement 21st century. But if we have to point out trivialities like this, we should do so if wesave the rapid decline that will lead us to the another medieval era.
I see this inability to distinguish between fundamentals and conventions each and every day in the university. Sadly, we all blame students. We blame poor elementary education. We blame politicians. But we should blame ourselves as teachers. I do encounter many professors who themselves cannot distingush between fundamentals and conventions. They pass on the wrong message to the students. And the result is catastrophic.
Let me give an example of poor teaching that cannot distinguish between fundamentals and conventions. Suppose a lecturer in a basic Statistics course tells students that sums of large numbers behave as if they come from a normal distribution without making the effort to explain (a) the assumptions or (b) why the normal distribution is unavoidable. I am well aware of the mathematical difficulties of such a concept for a beginning Statistics course, but I am also well aware of methods that can convey the message to the students without having to go through a stern mathematical demonstration. Such methods, unavoidably, will leave students with questions. But this is the point of education: students should be left with (the right) questions so that they will seek to fill in the gaps themselves or by attending more advanced courses. Instead, what is happening in many institutions of so-called higher education (and, indeed, in mathematical sciences departments), is that lazy (or ignorant?) lecturers will fill the students' minds with wrong impressions such as: Statistics means opening an excel programme, filling in the squares with data, and pressing a few buttons to get an answer. How boring! But how convenient if your utility function is to mazimize profit by having lots of students enrol in your classes. And how well it works for those students who choose the path of least action.
An example of a fundamental truth is the inverse square law of gravity. It is an empirical fact, based on observation, experiment, measurements; by accepting it, we build a theory upon which we can predict other facts, understand why it takes about 365 days for the earth to go around the sun, and build satellites, among other things. This is why the law of gravity is fundamental.
An example of a convention is that a week has seven days. It surprises many people that the concept of a week is not a concept, but a rather arbitray convention. It is difficult for many to digest this because the concept has been around for, well, some four thousand years. Of course, there are many a posteriori justifications. Why, say some, the week consists of seven days because the Bible says so. This is not a justification, even if the Bible was written by a God, as many contend.
The inability to distinguish between a fundamental truth and a convention is a major problem. It suddens me to have to point this out to my students (and others), in the post-enlightenement 21st century. But if we have to point out trivialities like this, we should do so if wesave the rapid decline that will lead us to the another medieval era.
I see this inability to distinguish between fundamentals and conventions each and every day in the university. Sadly, we all blame students. We blame poor elementary education. We blame politicians. But we should blame ourselves as teachers. I do encounter many professors who themselves cannot distingush between fundamentals and conventions. They pass on the wrong message to the students. And the result is catastrophic.
Let me give an example of poor teaching that cannot distinguish between fundamentals and conventions. Suppose a lecturer in a basic Statistics course tells students that sums of large numbers behave as if they come from a normal distribution without making the effort to explain (a) the assumptions or (b) why the normal distribution is unavoidable. I am well aware of the mathematical difficulties of such a concept for a beginning Statistics course, but I am also well aware of methods that can convey the message to the students without having to go through a stern mathematical demonstration. Such methods, unavoidably, will leave students with questions. But this is the point of education: students should be left with (the right) questions so that they will seek to fill in the gaps themselves or by attending more advanced courses. Instead, what is happening in many institutions of so-called higher education (and, indeed, in mathematical sciences departments), is that lazy (or ignorant?) lecturers will fill the students' minds with wrong impressions such as: Statistics means opening an excel programme, filling in the squares with data, and pressing a few buttons to get an answer. How boring! But how convenient if your utility function is to mazimize profit by having lots of students enrol in your classes. And how well it works for those students who choose the path of least action.
21 October 2008
Religion (Greek Orthodox style) via mobile phones!
This posting requires little explanation. The sheer idiocy of (this kind, but not only...) religious practice is so blatant that only a moron would not see it.
Caption of picture on the left:
DOWNLOAD TO YOUR MOBILE
THE HOLY ICON YOU WISH
TO PROTECT YOU!
(Incidentally, the first fellow on the fifth row is Aghios Nectarios and I am at distance 2 from him, for he was the teacher of my grandfather in a boarding school. In other words, I have direct link to saints; I need no mobile phone.)
Caption of picture on the right:
THE USE
OF MOBILE PHONES
INSIDE THE CHURCH
PROHIBITS
COMMUNICATION WITH GOD
PLEASE
SWITCH IT OFF
Actually, the right picture poses a certain challenge. Does it actually say that one cannot communicate with God via mobile telephony? Should we blame mobile phones? Should we blame the bad use of them? Does it, perhaps, say that if one uses mobile phones in a certain manner in a church then he or she can actually communicate with God? I wouldn't be surprised if the latter was actually meant. It is well-known that, for decades now, Americans have been communicating with God via TV. So why not via a cell phone? They are both communication media based on electromagnetic waves. I would guess that God can be reached around the frequency of 10^8 Hz, although I could be wrong. It would be an interesting Science project to find out God's frequency band. If you happen to know it, please let me know. I'll pass on the information to the Greek Orthodox church.
Thank you.
Caption of picture on the left:
DOWNLOAD TO YOUR MOBILE
THE HOLY ICON YOU WISH
TO PROTECT YOU!
(Incidentally, the first fellow on the fifth row is Aghios Nectarios and I am at distance 2 from him, for he was the teacher of my grandfather in a boarding school. In other words, I have direct link to saints; I need no mobile phone.)
Caption of picture on the right:
THE USE
OF MOBILE PHONES
INSIDE THE CHURCH
PROHIBITS
COMMUNICATION WITH GOD
PLEASE
SWITCH IT OFF
Actually, the right picture poses a certain challenge. Does it actually say that one cannot communicate with God via mobile telephony? Should we blame mobile phones? Should we blame the bad use of them? Does it, perhaps, say that if one uses mobile phones in a certain manner in a church then he or she can actually communicate with God? I wouldn't be surprised if the latter was actually meant. It is well-known that, for decades now, Americans have been communicating with God via TV. So why not via a cell phone? They are both communication media based on electromagnetic waves. I would guess that God can be reached around the frequency of 10^8 Hz, although I could be wrong. It would be an interesting Science project to find out God's frequency band. If you happen to know it, please let me know. I'll pass on the information to the Greek Orthodox church.
Thank you.
19 October 2008
Physics vs Management
As I was flying back home, I spent a few hours at the Amsterdam airport. One of my favourite activities is to visit the business section of the bookshop and look at amusing titles such as "the path to leadership", "how to make money while sleeping", "management and zen", "the habits of the fifty five most successful people in Saudi Arabia", and so on. Last year I came across a book on finance (still in the business section) which contained a statement of the Black Scholes formula, followed by a programme in Excel. It is then when I realised that it is good I don't do financial mathematics.
The main point today of this comment is the following image, taken as Schiphol a few hours ago:
Imagine seeing these two books, in the same series, next to each other at the formative age of, say, fifteen. And suppose you had no hunch for science. You'd instantly think that management is as deep as physics or, at least, something that can be studied at the same level as physics. You go to university, you have a choice: Should I study this or that? You have forgotten you've seen these two covers, but it's embedded in you. You believe that there is a choice. And that it is, merely, a choice between equivalent subjects.
This is what the modern university is like. This is what our administrators promote. Science has become equivalent to making money for, hm... for what, really?
The main point today of this comment is the following image, taken as Schiphol a few hours ago:
Imagine seeing these two books, in the same series, next to each other at the formative age of, say, fifteen. And suppose you had no hunch for science. You'd instantly think that management is as deep as physics or, at least, something that can be studied at the same level as physics. You go to university, you have a choice: Should I study this or that? You have forgotten you've seen these two covers, but it's embedded in you. You believe that there is a choice. And that it is, merely, a choice between equivalent subjects.This is what the modern university is like. This is what our administrators promote. Science has become equivalent to making money for, hm... for what, really?
18 October 2008
On the Platonic existence of numbers
Yesterday I came across an introductory paper by Olle Häggström, Objective truth versus human understanding in mathematics and in chess (2007), The Montana Math. Enthusiast. In it, Olle supports two ideas, both of which I have always held firmly. First that numbers exist independently of humans, and second that the human way of doing mathematics will always play a role in it and, no matter how advanced our computational machines turn out to be, they will never substitute the way we think, we prove and, more importantly, we understand mathematics (and science more generally).
Olle questions whether the first philosophical idea (the platonic ecistence of numbers) can be as dangerous as the following argument for the existence of God: " To anyone who has met God, His existence can no longer be in doubt. " I don't think so. Of course, accepting the existence of numbers as independent of humans goes beyond the realm of science and mathematics, but it is not dangerous. In fact, what Olle does not mention in his article is that we did have a whole system, a religion if you wish, that was based, precisely, on the concept of number as a divine object: Why, Pythagoras himself established his school which lasted for 600 years before it was destroyed by early Christians (they stoned to death the last of the Pythagorean mathematicians, Hypatia of Alexandria). I maintain that we would have ended up with a much better society had numbers still been the object of divinity, rather than a merciless God. I would definitely go to church every Sunday (or Saturday or Friday...) if we were to discuss numbers, and discuss I mean, rather than listen (without the possibility of asking any deep questions) to a boring priest, minister, rabbi, etc, and performal silly rituals.
Anyway, I'm digressing. Back to Olle's article, I would like to add that if we accept that numbers are independent of the human experience then we quickly reach the fact that it is merely the empty set that is the only thing that exists. Indeed, all numbers can be constructed from the integers which themselves can be constructed from the empty set, which I here denote by o. Indeed, zero is defined as o. One is defined as the set that contains o. Two is defined as the set that contains o and 1, and so on: Integer n is defined as the set containing all the previous integers. This model is, arguably, the best we have: It leads naturally to the construction of transfinite ordinals (Cantor) as well as surreal numbers (Conway). The latter ones are representations of two-player strategic games, just as the game of chess that Olle discusses in his paper.
So, the empty set is all there is then. Do you hear some reverberations of Zen Buddhism or Ancient Taoism? Hm, yes, indeed. Not that I will take these systems too seriously, but they do rely on the concepts of emptiness and nothingness, respectively.
As for whether Maths is human or not, I do agree again with Olle in that it is not the building stones of Mathematics that are human, but it is the way we do it that is. We, as humans, have to decide what to study, what to accept, what to prove, how to prove it, how to interpret and understand a proof, and how to use a certain result. Suppose we had reached a stage where we could solve all ordinary differential equations of the form
P(D)y = z
where P is a polynomial with real coefficients of degree less than 40, z=z(x) is a given function of one real variable x, y=y(x) is the unknown function, while D is the derivative operator. But say that the explicit solution required a few thousand of pages to write down. So? Would we accept it as an answer? Certainly not! Who says so? Why, everyone, mathematicians, engineers, physicists, practitioners... Only a robot would seriously maintain that a 1000-page formula is an answer. The reason for our dislike of such a formula is, precisely, because of our physical (and therefore mental) limitations. One could, possibly, imagine another world, where "humans" were 4 times as tall, with eyes 3 times as big, brain 5 times as large, and so on. Then mathematics would have been different. This is a bit of a naive explanation, but does convey my point.
Take another example. In Maths, we are interested in rates of convergence. What does this mean? It means to find out how fast a certain sequence converges. But the answer, i.e. the rate of convergence, must be given in terms of an "elementary" function, i.e. a polynomial, an exponential, and so on--only a handful of them, or in terms of another function we understand. Again, this is because of our human understanding of what constitutes elementary.
Let me also mention that (many) mathematicians are often faced with a choice: should we study this or that? Why should we accept or reject the axiom of choice? (Axioms are, roughly speaking, statements that cannot be proved or disproved, based on previously accepted statements.) If we do, we get a certain kind of Maths. If we don't we get another. What is better? Again, the answer is beyond the field of Mathematics. It has to do with us, humans, with the way we want to interpret the world, with the machines we need to construct, the tools to use to cook better food, etc.
I find the quotation, in Olle's paper, of a statement of Gowers interesting:
Namely, that we can live without the idea that an ordered pair (x,y) really is a funny set of the form {{x},{x,y}}, and that undergraduates would be confused by it.
Why should we need to take one point of view? I do agree with Gowers that, esp. nowadays, most undergraduates would get confused. And that when we introduce an ordered pair we do have to say the obvious thing, instead of reducing it to set theory. At least not immediately. But I do maintain (and have often found useful) to have the ability to reduce intuitively understood concepts to its fundamentals, to the axioms and objects of set theory, say. I take no sides. I maintain that both rigour and intuition are absolutely necessary. I am not surprised that Gowers seems to be taking on one side only. His colleague, Alan Baker, writes in the preface of his wonderful book, A Concise Introduction to the Theory of Numbers , Cambridge U. Press (1985), that "[t]there is no need to enter here into philosophical questions concerning the existence of [the integers]". He is right: his book is a wonderful speedy introduction to those aspects of number theory that lead to the solvability of Diophantine equations. Diophantus (from the works of whom--destroyed by early Christians, preserved by Arabs--all modern Algebra stems) has discovered algorithms for solving (systems) of classes of polynomial equations in integers. He didn't care about the existence of integers: Integers did exist and if you dared accept that square root of 2 was irrational you might lose your head. But Baker adds the adverb "here" in his sentence. He means, I hope, that elsewhere, at some other time, the student might wish to question the existence of integers, wonder why they should exist and convince herself or himself that they do (or do not!).
This is why Science and Mathematics is much more desirable than blind faith: we discuss, we question, we argue, we come to a conclusion, we revise, we discuss again, all along based on proofs and physical evidence.
Olle says (and I find this amazing!) that Freeman Dyson maintains that the statement "there exists a power of two, 2^n, such that, when written in decimal and read backwards it is a power of 5" is not provable!
It is quite rare that we encounter statements that are unprovable. Although, from a counting point of view, most statements within a mathematical system should be independent of its axiomatic foundation, it is very hard to bump into one. Is that not then another evidence supporting the idea that the way we do Mathematics, the way we seek to discover (for discoverers we are) truth within its vast archipelago, is, indeed, very human-based?
Olle questions whether the first philosophical idea (the platonic ecistence of numbers) can be as dangerous as the following argument for the existence of God: " To anyone who has met God, His existence can no longer be in doubt. " I don't think so. Of course, accepting the existence of numbers as independent of humans goes beyond the realm of science and mathematics, but it is not dangerous. In fact, what Olle does not mention in his article is that we did have a whole system, a religion if you wish, that was based, precisely, on the concept of number as a divine object: Why, Pythagoras himself established his school which lasted for 600 years before it was destroyed by early Christians (they stoned to death the last of the Pythagorean mathematicians, Hypatia of Alexandria). I maintain that we would have ended up with a much better society had numbers still been the object of divinity, rather than a merciless God. I would definitely go to church every Sunday (or Saturday or Friday...) if we were to discuss numbers, and discuss I mean, rather than listen (without the possibility of asking any deep questions) to a boring priest, minister, rabbi, etc, and performal silly rituals.
Anyway, I'm digressing. Back to Olle's article, I would like to add that if we accept that numbers are independent of the human experience then we quickly reach the fact that it is merely the empty set that is the only thing that exists. Indeed, all numbers can be constructed from the integers which themselves can be constructed from the empty set, which I here denote by o. Indeed, zero is defined as o. One is defined as the set that contains o. Two is defined as the set that contains o and 1, and so on: Integer n is defined as the set containing all the previous integers. This model is, arguably, the best we have: It leads naturally to the construction of transfinite ordinals (Cantor) as well as surreal numbers (Conway). The latter ones are representations of two-player strategic games, just as the game of chess that Olle discusses in his paper.
So, the empty set is all there is then. Do you hear some reverberations of Zen Buddhism or Ancient Taoism? Hm, yes, indeed. Not that I will take these systems too seriously, but they do rely on the concepts of emptiness and nothingness, respectively.
As for whether Maths is human or not, I do agree again with Olle in that it is not the building stones of Mathematics that are human, but it is the way we do it that is. We, as humans, have to decide what to study, what to accept, what to prove, how to prove it, how to interpret and understand a proof, and how to use a certain result. Suppose we had reached a stage where we could solve all ordinary differential equations of the form
P(D)y = z
where P is a polynomial with real coefficients of degree less than 40, z=z(x) is a given function of one real variable x, y=y(x) is the unknown function, while D is the derivative operator. But say that the explicit solution required a few thousand of pages to write down. So? Would we accept it as an answer? Certainly not! Who says so? Why, everyone, mathematicians, engineers, physicists, practitioners... Only a robot would seriously maintain that a 1000-page formula is an answer. The reason for our dislike of such a formula is, precisely, because of our physical (and therefore mental) limitations. One could, possibly, imagine another world, where "humans" were 4 times as tall, with eyes 3 times as big, brain 5 times as large, and so on. Then mathematics would have been different. This is a bit of a naive explanation, but does convey my point.
Take another example. In Maths, we are interested in rates of convergence. What does this mean? It means to find out how fast a certain sequence converges. But the answer, i.e. the rate of convergence, must be given in terms of an "elementary" function, i.e. a polynomial, an exponential, and so on--only a handful of them, or in terms of another function we understand. Again, this is because of our human understanding of what constitutes elementary.
Let me also mention that (many) mathematicians are often faced with a choice: should we study this or that? Why should we accept or reject the axiom of choice? (Axioms are, roughly speaking, statements that cannot be proved or disproved, based on previously accepted statements.) If we do, we get a certain kind of Maths. If we don't we get another. What is better? Again, the answer is beyond the field of Mathematics. It has to do with us, humans, with the way we want to interpret the world, with the machines we need to construct, the tools to use to cook better food, etc.
I find the quotation, in Olle's paper, of a statement of Gowers interesting:
Namely, that we can live without the idea that an ordered pair (x,y) really is a funny set of the form {{x},{x,y}}, and that undergraduates would be confused by it.
Why should we need to take one point of view? I do agree with Gowers that, esp. nowadays, most undergraduates would get confused. And that when we introduce an ordered pair we do have to say the obvious thing, instead of reducing it to set theory. At least not immediately. But I do maintain (and have often found useful) to have the ability to reduce intuitively understood concepts to its fundamentals, to the axioms and objects of set theory, say. I take no sides. I maintain that both rigour and intuition are absolutely necessary. I am not surprised that Gowers seems to be taking on one side only. His colleague, Alan Baker, writes in the preface of his wonderful book, A Concise Introduction to the Theory of Numbers , Cambridge U. Press (1985), that "[t]there is no need to enter here into philosophical questions concerning the existence of [the integers]". He is right: his book is a wonderful speedy introduction to those aspects of number theory that lead to the solvability of Diophantine equations. Diophantus (from the works of whom--destroyed by early Christians, preserved by Arabs--all modern Algebra stems) has discovered algorithms for solving (systems) of classes of polynomial equations in integers. He didn't care about the existence of integers: Integers did exist and if you dared accept that square root of 2 was irrational you might lose your head. But Baker adds the adverb "here" in his sentence. He means, I hope, that elsewhere, at some other time, the student might wish to question the existence of integers, wonder why they should exist and convince herself or himself that they do (or do not!).
This is why Science and Mathematics is much more desirable than blind faith: we discuss, we question, we argue, we come to a conclusion, we revise, we discuss again, all along based on proofs and physical evidence.
Olle says (and I find this amazing!) that Freeman Dyson maintains that the statement "there exists a power of two, 2^n, such that, when written in decimal and read backwards it is a power of 5" is not provable!
It is quite rare that we encounter statements that are unprovable. Although, from a counting point of view, most statements within a mathematical system should be independent of its axiomatic foundation, it is very hard to bump into one. Is that not then another evidence supporting the idea that the way we do Mathematics, the way we seek to discover (for discoverers we are) truth within its vast archipelago, is, indeed, very human-based?
9 October 2008
Substitutes for religion
Many people say: "What can we do without religion? How can we have moral principles without it?"
Well, just substitute your prayer with a poem recitation. It is much better, because you don't have to subscribe to arbitrary dogmas, and, besides, poetry can be re-written and revised, if necessary, unlike religious texts that can never change.
Here is an example of a substitute for a religious practice then: recite this poem:
Ithaca
Well, just substitute your prayer with a poem recitation. It is much better, because you don't have to subscribe to arbitrary dogmas, and, besides, poetry can be re-written and revised, if necessary, unlike religious texts that can never change.
Here is an example of a substitute for a religious practice then: recite this poem:
Ithaca
An excellent recitation, by Sean Connery, of an English interpretation
of this most famous poem of Constantine Cavafy
of this most famous poem of Constantine Cavafy
Σα βγεις στον πηγαιμό για την Ιθάκη, να εύχεσαι νάναι μακρύς ο δρόμος, γεμάτος περιπέτειες, γεμάτος γνώσεις. Τους Λαιστρυγόνας και τους Κύκλωπας, τον θυμωμένο Ποσειδώνα μη φοβάσαι, τέτοια στον δρόμο σου ποτέ σου δεν θα βρεις, αν μέν’ η σκέψις σου υψηλή, αν εκλεκτή συγκίνησις το πνεύμα και το σώμα σου αγγίζει. Τους Λαιστρυγόνας και τους Κύκλωπας, τον άγριο Ποσειδώνα δεν θα συναντήσεις, αν δεν τους κουβανείς μες στην ψυχή σου, αν η ψυχή σου δεν τους στήνει εμπρός σου. Να εύχεσαι νάναι μακρύς ο δρόμος. Πολλά τα καλοκαιρινά πρωιά να είναι που με τι ευχαρίστησι, με τι χαρά θα μπαίνεις σε λιμένας πρωτοειδωμένους· να σταματήσεις σ’ εμπορεία Φοινικικά, και τες καλές πραγμάτειες ν’ αποκτήσεις, σεντέφια και κοράλλια, κεχριμπάρια κ’ έβενους, και ηδονικά μυρωδικά κάθε λογής, όσο μπορείς πιο άφθονα ηδονικά μυρωδικά· σε πόλεις Aιγυπτιακές πολλές να πας, να μάθεις και να μάθεις απ’ τους σπουδασμένους. Πάντα στον νου σου νάχεις την Ιθάκη. Το φθάσιμον εκεί είν’ ο προορισμός σου. Aλλά μη βιάζεις το ταξείδι διόλου. Καλλίτερα χρόνια πολλά να διαρκέσει· και γέρος πια ν’ αράξεις στο νησί, πλούσιος με όσα κέρδισες στον δρόμο, μη προσδοκώντας πλούτη να σε δώσει η Ιθάκη. Η Ιθάκη σ’ έδωσε τ’ ωραίο ταξείδι. Χωρίς αυτήν δεν θάβγαινες στον δρόμο. Άλλα δεν έχει να σε δώσει πια. Κι αν πτωχική την βρεις, η Ιθάκη δεν σε γέλασε. Έτσι σοφός που έγινες, με τόση πείρα, ήδη θα το κατάλαβες η Ιθάκες τι σημαίνουν. | As you set out for Ithaca, hope that you journey is a long one, full of adventure full of discovery. Laistrygonians and Cyclops, and great Poseidon do not be afraid of them, you'll never find things like that on your way, as long as you keep your thoughts raised high, as long as a rare sensation touches your spirit and your body. Laistrygonians and Cyclops, wild Poseidon you won't encounter them, unless you bring them along inside your soul, unless your soul sets them up in front of you. Hope that your journey is a long one. May there be many summer mornings when with what pleasure, what joy you come into harbour scene for the first time; may you stop at Phoenician trading stations, to buy fine things, mother-of-pearl, coral, amber, and ebony, sensual perfume of ever kind, as many sensual perfumes as you can; and may you visit many Egyptian cities, to learn and learn again from those who know. Keep Ithaca always in you mind. Arriving there is what you are destined for, But do not hurry the journey at all. Better if it lasts for years; so that you are old by the time you reach the island, wealthy with all you have gained on the way, not expecting Ithaca to make you rich. Ithaca gave you the marvellous journey. Without her you would not have set out. She has nothing left to give you now. And if you find her poor, Ithaca won't have fooled you. Wise as you will have become, so full of experience, you will have understood by then what these Ithacas mean. |
9/10/08... Happy Yom Kippur to my Jewish friends!
23 May 2008
A funny job posting
Allegedly, around 1990, the Southeast Missouri State Universiry, posted an announcement for a faculty position in philosophy, which is extremely funny (and sincere).
Some excerpts:
We are more interested in [...] cansidates with real teaching experience than in newly minted PhD's who might have unrealistic expectations for academic growth at an institution such as ours.
Our students tend to be poorly prepared [...], intellectually passive, interested primarily in partying, and culturally provincial [...]
[Our] academic enviroment is distinctly non-intellectual [...]
What an honest advertisement! I know many departments who are just like that. But would they ever dare to advertise a job thus?
Some excerpts:
We are more interested in [...] cansidates with real teaching experience than in newly minted PhD's who might have unrealistic expectations for academic growth at an institution such as ours.
Our students tend to be poorly prepared [...], intellectually passive, interested primarily in partying, and culturally provincial [...]
[Our] academic enviroment is distinctly non-intellectual [...]
What an honest advertisement! I know many departments who are just like that. But would they ever dare to advertise a job thus?
20 May 2008
Origami Pentagon, ctd.
Actually, I know one quick and dirty method (which my father had told me once): take a strip of paper of constant width w and tie a knot, as in the figure. Flatten the knot carefully so that it leaves no gaps--it should all fit nicely together. The result is a regular pentagon of edge length w.
Origami Pentagon
A regular dodecahedron has faces which are regular pentagons. Looking around for a good method to construct pentagons by paper folding I came across one which seemed nice. Unfortunately, the method is not exact (as often purported to be) but only approximate. The approximation is good, but, if on top of the mathematical error one adds the physical one, the resulting pentagon is often visibly non-canonical.
The approximate method can be described as follows:
Start with a square. Let A, B be the middle points of two adjacent sides and C the vertex farthest away from these two points. Let M be the middle of the segment BC. Consider the shaded rectangle whose diagonal is MC and rotate it 90 degrees counterclockwise so C goes to C1. Pick the point K so that KC1:KM = 1:3. The "pentagon" has vertices A, B, C, K and the symmetric of K.
To see that it's not a regular pentagon, let the side of the original square have length 8u where u is the square root of 2 (for no good reason other than that I wanted to end up with integers). Then, using the Pythagorean theorem several times, we can see that AB equals sqrt(256)=16, but BK equals sqrt(250) which equals 15.81... (Pretty good approximation.) Notice that MK passes through the middle of BC and is perpendicular to it, so BK equals CK. By symmetry, 4 of the 5 sides of the pentagon have length 15.81... and only one has length 16.
Does anyone know an exact (and simple...) origami method for constructing regular pentagons?
The approximate method can be described as follows:
Start with a square. Let A, B be the middle points of two adjacent sides and C the vertex farthest away from these two points. Let M be the middle of the segment BC. Consider the shaded rectangle whose diagonal is MC and rotate it 90 degrees counterclockwise so C goes to C1. Pick the point K so that KC1:KM = 1:3. The "pentagon" has vertices A, B, C, K and the symmetric of K.To see that it's not a regular pentagon, let the side of the original square have length 8u where u is the square root of 2 (for no good reason other than that I wanted to end up with integers). Then, using the Pythagorean theorem several times, we can see that AB equals sqrt(256)=16, but BK equals sqrt(250) which equals 15.81... (Pretty good approximation.) Notice that MK passes through the middle of BC and is perpendicular to it, so BK equals CK. By symmetry, 4 of the 5 sides of the pentagon have length 15.81... and only one has length 16.
Does anyone know an exact (and simple...) origami method for constructing regular pentagons?
Modern miracles
People think that miracles do not happen in our days. Wrong! Here is some multi-faith proof:
From left to right:
- Cactus displays Allah in arabic.
- The image of Virgin Mary on a toast.
- Statue of Lord Ganesha consumes milk.
From left to right:
- Cactus displays Allah in arabic.
- The image of Virgin Mary on a toast.
- Statue of Lord Ganesha consumes milk.
19 May 2008
Can you believe that?
I've often heard that football fans refer to their favourite team in religious terms. This is a kind of metaphor. Or is it not?
Apparently not. I'm not a sociologist but I'm almost convinced that the type of faith certain people have towards, say, their favourite sports team or political party is very similar (biologically?) to a religious faith.
In Argentina, football fans have taken a step closer towards establishing a firm link between sports faith and religious faith. They established the Church of Maradona-God's Hand or Iglesia Maradoniana-la Mano de Dios, that reveres the football player Diego Maradona. One of its founders, Alejandro Verón, says: “I have a rational religion and that’s the Roman-catholic church, and I have a religion passed on my heart, passion, and that’s Diego Maradona."
(Why, exactly, the catholic church constitutes a rational religion requires closer examination...)
--- --- ---
It may be argued that reverence is not towards football but towards a specific person. So it behooves us to ask whether we can find another example of religious faith towards a living person. We don't have to go too far. Prince Philip, Duke of Edinburgh (the Queen's husband), is the God of the Vanuatu people in South Pacific.
Prince Philip is apparently well aware that he serves as God, so he makes sure that, from time to time, his photographs are shipped over to the Vanuatu people.
Any comments?
Apparently not. I'm not a sociologist but I'm almost convinced that the type of faith certain people have towards, say, their favourite sports team or political party is very similar (biologically?) to a religious faith.
In Argentina, football fans have taken a step closer towards establishing a firm link between sports faith and religious faith. They established the Church of Maradona-God's Hand or Iglesia Maradoniana-la Mano de Dios, that reveres the football player Diego Maradona. One of its founders, Alejandro Verón, says: “I have a rational religion and that’s the Roman-catholic church, and I have a religion passed on my heart, passion, and that’s Diego Maradona."
(Why, exactly, the catholic church constitutes a rational religion requires closer examination...)
--- --- ---
It may be argued that reverence is not towards football but towards a specific person. So it behooves us to ask whether we can find another example of religious faith towards a living person. We don't have to go too far. Prince Philip, Duke of Edinburgh (the Queen's husband), is the God of the Vanuatu people in South Pacific.
Prince Philip is apparently well aware that he serves as God, so he makes sure that, from time to time, his photographs are shipped over to the Vanuatu people.
Any comments?
18 May 2008
Quantum mechanical ... healing!
The misuse of science for achieving one's goal has been always been practiced by many. However, nowadays, anybody can get instant information on any scientific subject, just by googling or wikipeding a term they've heard.
And some people make real money from bogus science...
I'm especially amused by the "use" of Quantum Mechanics: it appears to have entered the realm of psychotherapy. Here are a couple of examples:
First, there is some Sandra Anne Taylor, who has published a book called "Quantum Success". In it, she claims that
Through quantum physics, we know that reality isn’t separate from the observation of it, and the same is true for our own lives. What we experience in the real world can’t be separated from our perception of it. In fact, the study of biomechanics reveals that the brain isn’t even capable of distinguishing the difference between reality and memory.....
When people understand the human application of quantum physics, they can see that their consciousness, energy, and intention carry great power in the consequences of their lives. But when it comes to success, most people want to know, “What’s love got to do with it?”
She explains, however, that:
... The Law of Magnetism. Love is the single most magnetic energy that you can project.
Sandra Anne Taylor has, obviously, no understanding quantum physics or magnetism. She just makes money by selling her products to people who are fascinated by the mystique of grandiose scientific words.
---
Here's another example (I learned this from Shallit's blog): Dr. Richard Bartlett D.C., N.D., makes money with his Matrix Energetics. He goes around and charges 500+ dollars for each "seminar" in which he makes participants attain the Quantum Field at their fingertips, make instant physical, observable changes, create quick observable changes with no waiting and no running energy...
Here is a most funny quote of Dr. Richard Bartlett D.C., N.D.:
"There’s something called the Heisenberg Uncertainty Principle. What that says, essentially, is you cannot observe a system without entering into that observation and therefore changing it. Scientifically, this means that if you look at something and attempt to measure its velocity, you lose track of its actual location. If you try and track its location, you lose the ability to measure its velocity. You can never actually measure both at the same time; you can observe one and change the other."
---
But the use of science is not restricted to psychobogustherapy. It is also used for religious purposes. And not by people who have no understanding of science, but by scientists themselves. I really don't mind much about simpletons (?) like Taylor and Bartlett when they "use" quantum physics" for "healing" purposes: they just take advantage of sick people who are willing to pay money to be quantumphysicallyhealed. They just (ab)use the rules of free market. But it disturbes me greatly when I find out that a scientist uses science to prove bogus concepts. More about that in my next posting...
And some people make real money from bogus science...
I'm especially amused by the "use" of Quantum Mechanics: it appears to have entered the realm of psychotherapy. Here are a couple of examples:
First, there is some Sandra Anne Taylor, who has published a book called "Quantum Success". In it, she claims that
Through quantum physics, we know that reality isn’t separate from the observation of it, and the same is true for our own lives. What we experience in the real world can’t be separated from our perception of it. In fact, the study of biomechanics reveals that the brain isn’t even capable of distinguishing the difference between reality and memory.....
When people understand the human application of quantum physics, they can see that their consciousness, energy, and intention carry great power in the consequences of their lives. But when it comes to success, most people want to know, “What’s love got to do with it?”
She explains, however, that:
... The Law of Magnetism. Love is the single most magnetic energy that you can project.
Sandra Anne Taylor has, obviously, no understanding quantum physics or magnetism. She just makes money by selling her products to people who are fascinated by the mystique of grandiose scientific words.
---
Here's another example (I learned this from Shallit's blog): Dr. Richard Bartlett D.C., N.D., makes money with his Matrix Energetics. He goes around and charges 500+ dollars for each "seminar" in which he makes participants attain the Quantum Field at their fingertips, make instant physical, observable changes, create quick observable changes with no waiting and no running energy...
Here is a most funny quote of Dr. Richard Bartlett D.C., N.D.:
"There’s something called the Heisenberg Uncertainty Principle. What that says, essentially, is you cannot observe a system without entering into that observation and therefore changing it. Scientifically, this means that if you look at something and attempt to measure its velocity, you lose track of its actual location. If you try and track its location, you lose the ability to measure its velocity. You can never actually measure both at the same time; you can observe one and change the other."
---
But the use of science is not restricted to psychobogustherapy. It is also used for religious purposes. And not by people who have no understanding of science, but by scientists themselves. I really don't mind much about simpletons (?) like Taylor and Bartlett when they "use" quantum physics" for "healing" purposes: they just take advantage of sick people who are willing to pay money to be quantumphysicallyhealed. They just (ab)use the rules of free market. But it disturbes me greatly when I find out that a scientist uses science to prove bogus concepts. More about that in my next posting...
9 March 2008
Welcome to my first blog
I am opinionated. This means I am alive. Everyone should be so. I've been thinking, for a while, instead of trying to smuggle things into my professional webpage, I should create a blog. I never tried to.
one another out and copying from one another. So, I thought, if he
can do it, then why not me? And I did. Here is my first attempt then.
So, please go ahead and leave a comment.
I admit I got inspired by Jeffrey Shallit's `Recursivity' blog.
No he doesn't know it, but that's the beauty of the Internet: findingone another out and copying from one another. So, I thought, if he
can do it, then why not me? And I did. Here is my first attempt then.
So, please go ahead and leave a comment.
Disturbing realities at the dawn of the 21st century
The middle ages have supposedly gone by. Enlightenment has supposedly showed us that we can use reason to understand ourselves, the world, the nature, the mind; that we could (and should) go back to the origins of the so-called Western Civilization and resurrect what was lost for more than a thousand years.
Yet, a few unexpected things have recently happened and, despite their dissimilarities, they seem to be closely connected, pointing towards a grim future, unless.... unless we act, we remind ourselves of the principles that, only twenty years ago, we would take for granted. I'm referring to Science, to Reason, to Education, to our right to question authority, to Democracy, to Free Thought, Free Speech...
The unexpected things were
Supposedly, technology (e.g. transportation, communication), and especially the Internet, has brought people closer to one another. But has it?
Most people I come across to, could not care less.
They are happy to watch the rugby game, drink beer, do their job while keeping a boss happy, never ask questions, never read history but only have a vague idea of what happened when, never think about anything except, possibly, in a very myopic manner, accept lies if they are convenient for them, be afraid to express their opinion, be very afraid to speak, be very very afraid to speak freely... Fear, that's what I see, a hidden fear being slowly instilled within many individuals. Indeed, things seem, at a surface level, more progressive than in times past, but are they so? Or is it, merely, an institutionalized political correctness that drives us?
What should we do to stop getting back to a Dark Age?
Yet, a few unexpected things have recently happened and, despite their dissimilarities, they seem to be closely connected, pointing towards a grim future, unless.... unless we act, we remind ourselves of the principles that, only twenty years ago, we would take for granted. I'm referring to Science, to Reason, to Education, to our right to question authority, to Democracy, to Free Thought, Free Speech...
The unexpected things were
- Resurgence of religious fundamentalism
- Degrading of education at all levels and in many parts of the world
- Establishment of new ideals that young people should aspire for, mostly related to business concepts
- New types of wars
Supposedly, technology (e.g. transportation, communication), and especially the Internet, has brought people closer to one another. But has it?
Most people I come across to, could not care less.
They are happy to watch the rugby game, drink beer, do their job while keeping a boss happy, never ask questions, never read history but only have a vague idea of what happened when, never think about anything except, possibly, in a very myopic manner, accept lies if they are convenient for them, be afraid to express their opinion, be very afraid to speak, be very very afraid to speak freely... Fear, that's what I see, a hidden fear being slowly instilled within many individuals. Indeed, things seem, at a surface level, more progressive than in times past, but are they so? Or is it, merely, an institutionalized political correctness that drives us?
What should we do to stop getting back to a Dark Age?
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